Coordinate Reference Research Articles

The wonderful world of relativity: a precise guide for the general reader

1. Introduction 2. A preview: the Laws of Motion 3. Something odd is happening all around us 4. Spacetime 5. Reference frames and coordinates 6. The basic principles of Relativity 7. Foundations re-explored. 8. Navigating in spacetime 9. Faster than light 10. Introduction to momentum and energy 11. Conclusion

SU-E-J-170: Clinical Evaluation of Positioning Accuracy of Two Immobilization Devices for Stereotactic Body Radiotherapy Using Cone Beam CT.

To evaluate the patient positioning accuracy and reproducibility of two commercially available immobilization systems for Stereotactic Body Radiotherapy (SBRT) treatment. Forty one patients with lung (n=21) or liver (n=20) malignancies were assigned to one of the two immobilization devices: Elekta stereotactic body frame (SBF) with built-in stereotactic coordinate system and Civco modular indexing based frame (MIF) without stereotactic reference. All patients underwent the same simulation and planning procedure followed by cone beam CT (CBCT) guided treatment setup. A total of 151 CBCT images were analyzed. The systematic and random isocenter setup errors of the two systems were calculated and compared based on the daily setup corrections under CBCT guidance. There was not statistically significant difference between the two systems in terms of systematic setup errors in all three translational directions, for both lung and liver patients. The random errors for the lung patients under SBF setup were 1.8mm, 2.0mm and 2.9mm for the vertical, longitudinal and lateral directions, respectively compared to 3.6mm, 4.1mm, and 4.2mm for MIF. A similar trend was also observed for liver patients. The random errors of liver MIF setup reached 3.5mm, 6.1mm and 5.7mm for the vertical, longitudinal and lateral directions, respectively, with relatively smaller errors 1.7mm, 3.4mm and 2.6mm with SBF setup. Repeated CBCTs occurred for MIF system in 42.4% and 40.7% of the lung and liver treatment to verify couch corrections based on the institutional tolerance, resulting in prolonged setup time. Only 25% and 13.6% of the lung and liver treatment with SBF required with repeated CBCT. Without stereotactic coordinate reference, the body frame system tended to have larger random setup errors and patient positioning accuracy inevitably relies on the volumetric imaging guidance. Patient comfort and reproducibility should be clearly considered for selecting a system.

The transformation between τ and TCB for deep space missions under IAU resolutions

For tracking spacecraft and performing radio science, the transformation between the proper time (τ) given by a clock carried onboard a spacecraft and the barycentric coordinate time (TCB) is investigated under IAU resolutions. In order to more clearly demonstrate manifestations of a physical model and improve computational efficiency, an analytic approach is adopted. After numerical verification, it is confirmed that this method is adequate to describe a Mars orbiter during one year, and is particularly good at describing the influence from perturbing bodies. Further analyses demonstrate that there are two main effects in the transformation: the gravitational field of the Sun and the velocity of the spacecraft in the barycentric coordinate reference system. The combined contribution of these effects is at the level of a few sub-seconds.

Heat transfer and entropy generation analyses associated with mixed electrokinetically induced and pressure-driven power-law microflows

In the present study, the first and second law analyses associated with combined pressure-driven and electroosmotic flow of power-law liquids through a uniform microannulus are performed numerically. In the first law analysis, the Poisson–Boltzmann and incompressible Navier–Stokes–Fourier (NSF) equations in the cylindrical polar coordinate reference frame as the governing equations are numerically solved using a finite difference method. The obtained velocity and temperature distributions are then employed to evaluate the associated Nusselt number, while simultaneous effects of viscous dissipation and Joule heating are taken into consideration. In the second law analysis, the relevant general expression for the entropy generation process is derived and the contributions of thermal diffusion, fluid friction and Joule heating irreversibility to the total entropy generation in the micro domain are examined. Finally, the variations of the aforementioned major variables with influential parameters such as the aspect ratio of the annuli, flow behavior index, dimensionless Debye–Hückel parameter, forcing ratio, dimensionless viscous heating parameter, and dimensionless Joule heating parameter are investigated.

Scene Graph Based Approach for Interoperable Virtual Globes

In this paper, a concept for developing and setting up virtual globes is discussed, which is based on principles of interoperable 3D spatial data infrastructures. Open geospatial industry standards for data and web services are merged with computer graphics technology to create a global coherent framework for accessing and displaying 3D assets. The author discusses how the scene graph concept can be used in a Geoweb environment. The Web 3D Service (W3DS) interface is used for streaming data in a distributed web architecture. Using scene graph data structures for encoding, transmitting, and displaying city- and landscape models imposes new requirements to geospatial analysis. The support of transformations between coordinate reference systems is essential in this context. Scene graph transformations are described in detail including matrix calculations. X3D is discussed as potential exchange format. Experiments were conducted using freely available data of OpenStreetMap and SRTM.

Automatic Registration of High-Resolution Images Using Local Properties of Features

We propose an automatic image-to-image registration of high-resolution satellite images using local properties and geometric locations of control points to improve the registration accuracy. First, coefficients of global affine transformation between images are extracted using a scale-invariant feature transform (SIFT)-based method, and features of the sensed image are transformed to the reference coordinate system using these coefficients. Then, a spatial distance and orientation difference between features of the reference and sensed images are additionally used to extract a large number of evenly distributed control points. The specified spatial distance is calculated between features of the sensed image that have been transformed to the reference coordinates and features of the reference image. Finally, the spatial distance integrated with Euclidean distances of invariant vectors is employed for local matching. The average orientation differences between control points of the two images are used for outlier elimination. A mapping function model consisting of an affine transformation and piecewise linear functions is applied to the control points for automatic registration of high-resolution images. The proposed method can extract a larger number of spatially well-distributed control points than SIFT-based methods. The registration accuracy for all sites calculated from manually selected checkpoints has acceptable geometric accuracy at the pixel level.

A Novel Data Embedding Method Using Adaptive Pixel Pair Matching

This paper proposes a new data-hiding method based on pixel pair matching (PPM). The basic idea of PPM is to use the values of pixel pair as a reference coordinate, and search a coordinate in the neighborhood set of this pixel pair according to a given message digit. The pixel pair is then replaced by the searched coordinate to conceal the digit. Exploiting modification direction (EMD) and diamond encoding (DE) are two data-hiding methods proposed recently based on PPM. The maximum capacity of EMD is 1.161 bpp and DE extends the payload of EMD by embedding digits in a larger notational system. The proposed method offers lower distortion than DE by providing more compact neighborhood sets and allowing embedded digits in any notational system. Compared with the optimal pixel adjustment process (OPAP) method, the proposed method always has lower distortion for various payloads. Experimental results reveal that the proposed method not only provides better performance than those of OPAP and DE, but also is secure under the detection of some well-known steganalysis techniques.

The problem of temporal validity of reference coordinates in the context of reliability of the ETRS89 system realization in Poland

ABSTRACT The IAG (International Association of Geodesy) Sub-Commission for the European reference frame (EUREF) passed a resolution recommending application of the ETRF2000 frame as national realizations of the ETRS89 reference system during the XXth EUREF Symposium in Gävle (Sweden) in 2010. The PL-ETRF2000 system is comprised of EPN (EUREF Permanent Network) sites. Their coordinates and their temporal changes (velocities) were accurately determined on the basis of long-term GNSS observations. The transfer of the PLETRF2000 system onto the territory of Poland is realized by the ASG-EUPOS (Active Geodetic Network – European Position Determination System) permanent sites network. The ASG-EUPOS tasks include also system maintenance by continuous or periodical control of the coordinates and velocities constancy. According to the current Regulation of the Ministry of Administration and Digitization concerning geodesic, gravimetric and magnetic warps, the accuracy of sites of the fundamental warp (EPN sites belonging to ASG-EUPOS) may not be worse than 0.01 m for horizontal position and 0.02 m for geodesic height. It results in the necessity to monitor the performance of the reference sites for proper maintenance of the reference system. A new team for modeling deformations in Europe was established within the EUREF Working Group (The EUREF Working Group on Deformation Models) during the EUREF 2012 Symposium in Paris. One of its tasks is taking geo-kinematic models into consideration for national realizations of the ETRS89 and maximum usage of knowledge concerning the velocity field. The paper deals with the problem of temporal validity of the catalogue coordinates and the necessity of periodical updating them on the basis of velocities derived from long-term observations. Although Poland is located in a tectonically calm area and the intraplate velocities are small, some of the EPN and ASG-EUPOS sites have significant velocities and are subject to vertical movements. Lack of periodical updating of the coordinates realizing the reference system will cause lack of fulfillment of the assumed accuracy criterion. Analysis of horizontal and vertical velocities of sites belonging to the fundamental warp lead to assumption that two sites will exceed horizontal criterion in a period of time shorter than 10 years counting from the reference epoch (i.e. from 2011.0): KATO horizontal coordinates should be updated in 2014 and GWWL in 2021. Mores sites will exceed vertical criterion: BOGI (2021), GWWL (2015), KATO (2019), SWKI (2019) and ZYWI (2021). The vertical component updating will require of course changes of the horizontal component (coordinates are determined in the Cartesian orthogonal XYZ coordinate system and then recalculated for the ellipsoidal coordinates). Besides periodical coordinates updating it is recommended to conduct repeated processing for the entire network according to the EUREF standards for taking the current GNSS observations into consideration.

Determining Adequate Averaging Periods and Reference Coordinates for Eddy Covariance Measurements of Surface Heat and Water Vapor Fluxes over Mountainous Terrain

Two coordinate rotation approaches (double and planar-fit rotations) and no rotation, in association with averaging periods of 15 - 480 min, were applied to compute surface heat and water vapor fluxes using the eddy covariance approach. Measurements were conducted in an experimental watershed, the Lien-Hua-Chih (LHC) watershed, located in central Taiwan. For no rotation and double rotation approaches, an adequate averaging period of 15 or 30 min was suggested for better energy closure and small variations on energy closure fractions. For the planar-fit rotation approach, an adequate averaging period of 60 or 120 min was recommended, and a typical averaging period of 30 min is not superior to that of 60 or 120 min in terms of better energy closure and small variations on energy closure fractions. The Ogive function analysis revealed that the energy closure was improved with the increase of averaging time by capturing sensible heat fluxes at low-frequency ranges during certain midday hours at LHC site. Seasonal variations of daily energy closure fractions, high in dry season and low in wet season, were found to be associated with the surface dryness and strength of turbulent development. The mismatching of flux footprint areas among flux sensors was suggested as the cause of larger CF variations during the dry seasons as that indicated by the footprint analysis showing scattered source areas. During the wet season, the underestimation of turbulent fluxes by EC observations at the LHC site was attributed to weak turbulence developments as the source area identified by the footprint analysis was closer to the flux tower than those scattered in dry season.

Investigation of flow and heat transfer characteristics of rarefied gaseous slip flow in nonplanar micro-Couette configuration

In the present study the mechanism of transport phenomena in a low-speed rarefied gas flow confined between a shaft and its concentric housing, namely, the cylindrical Couette problem, is investigated analytically in the slip-flow regime. The incompressible Navier–Stokes–Fourier (NSF) equations in the cylindrical polar coordinate reference frame are employed while the simultaneous effects of viscous dissipation and rarefaction phenomenon are taken into account. Two different thermal boundary conditions are considered: the Uniform Heat Flux (UHF) and the Constant Wall Temperature (CWT). Solutions for the velocity and temperature distributions, the Nusselt number and the wall heat flux are obtained for different values of the Knudsen and Brinkman numbers and curvature parameter.

Modeling and Simulation of Electromechanical Coupling Dynamics for Permanent Magnet Synchronous AC Servomotor

Lagrange-Maxwell equations and Park transform are adopted based on electrical and mechanical energy equations consisting of servomotor parameters. Lagrange-Maxwell equations are transformed from three-phase stator reference coordinates to two-phase rotor reference coordinates. Electromechanical coupling dynamics equations of permanent magnet synchronous servomotor in two-phase reference coordinates are obtained. In this dynamical modeling method of electromechanical coupling system, to establish dynamical differential equations needs to measure amplitude of the flux induced by the permanent magnets and the winding's inductance in dq0 reference of the motor but needs not to measure the size of magnetic circuit. The equations deduced is terse, efficient, and the equations easy to use. Electromechanical coupling dynamics system, servomotor is simulated. Simulation results show that the electromechanical coupling dynamics equations deduced for servomotor are correct, and current control schemes are reasonable.

Investigation on the choice of boundary conditions and shape functions for flexible multi-body system

The objective of this investigation is to examine the correctness and efficiency of the choice of boundary conditions when using assumed mode approach to simulate flexible multi-body systems. The displacement field due to deformation is approximated by the Rayleigh-Ritz assumed modes in floating frame of reference (FFR) formulation. The deformations obtained by the absolute nodal coordinate (ANC) formulation which are transformed by two sets of reference coordinates are introduced as a criterion to verify the accuracy of the simulation results by using the FFR formulation. The relationship between the deformations obtained from different boundary conditions is revealed. Numerical simulation examples demonstrate that the assumed modes with cantilevered-free, simply-supported and free-free boundary conditions without inclusion of rigid body modes are suitable for simulation of flexible multi-body system with large over all motion, and the same physical deformation can be obtained using those mode functions, differ only by a coordinate transformation. It is also shown that when using mode shapes with statically indeterminate boundary conditions, significant error may occur. Furthermore, the slider crank mechanism with rigid crank is accurate enough for investigating boundary condition problem of flexible multi-body system, which cost significant less simulating time. The project was supported by the National Natural Science Foundation of China (10872126) and the Research Fund of the Doctoral Program of Higher Education of China (20100073110007).

Characterization of the 3D resolution of topometric sensors based on fringe and speckle pattern projection by a 3D transfer function

The increasing importance of optical 3D measurement techniques and the growing number of available methods and systems require a fast and simple method to characterize the measurement accuracy. However, the conventional approach of comparing measured coordinates to known reference coordinates of a test target faces two major challenges: the precise fabrication of the target and – in case of pattern projecting systems – finding the position of the reference points in the obtained point cloud. The modulation transfer function (MTF) on the other hand is an established instrument to describe the resolution characteristics of 2D imaging systems. Here, the MTF concept is applied to two different topometric systems based on fringe and speckle pattern projection to obtain a 3D transfer function. We demonstrate that in the present case fringe projection provides typically 3.5 times the 3D resolution achieved with speckle pattern projection. By combining measurements of the 3D transfer function with 2D MTF measurements the dependency of 2D and 3D resolutions are characterized. We show that the method allows for a simple comparison of the 3D resolution of two 3D sensors using a low cost test target, which is easy to manufacture.

The Novel Calibration Method for 3-DOF Measurement System

In this paper, a novel calibration method is developed to improve the measurement accuracy of 3-DOF measurement system. The squareness error between three sensors and misalignment error with respect to reference coordinate of machine tool are calibration parameters. To estimate these parameters, reference ball is used and moved in the measuring ranges of 3-DOF measurement system. The relation between calibration parameters, position of reference ball, measured data of sensors are defined using geometric constraint and estimated using least square method. Finally, simulation is done to check the feasibility of developed calibration method. The result of simulation revealed the validation of developed method.

Multi-robot olfactory search in structured environments

This paper presents a cooperative distributed approach for searching odor sources in unknown structured environments with multiple mobile robots. While searching and exploring the environment, the robots independently generate on-line local topological maps and by sharing them with each other they construct a global map. The proposed method is a decentralized frontier based algorithm enhanced by a cost/utility evaluation function that considers the odor concentration and airflow at each frontier. Therefore, frontiers with higher probability of containing an odor source will be searched and explored first. The method also improves path planning of the robots for the exploration process by presenting a priority policy. Since there is no global positioning system and each robot has its own coordinate reference system for its localization, this paper uses topological graph matching techniques for map merging. The proposed method was tested in both simulation and real world environments with different number of robots and different scenarios. The search time, exploration time, complexity of the environment and number of double-visited map nodes were investigated in the tests. The experimental results validate the functionality of the method in different configurations.

Intrinsic axes of partially coherent light beams and their invariance through rotationally symmetric ABCD optical systems

New transverse orthogonal axes associated with the beam shape are introduced on the basis of the irradiance-moment formalism that describes the overall spatial structure of partially coherent paraxial beams. We refer to them as the intrinsic axes of the beam. The angle between these axes and the laboratory reference coordinates can be determined from the measurements of the second-order spatial moments of the beam, even although the field amplitude is not analytically known. It has been found that the intrinsic axes remain invariant upon propagation through rotationally symmetric first-order optical systems. Two additional analytical quantities have also been introduced. One of them provides a measure of the beam symmetry, and the other one contains information about the beam rotation under propagation. When the field is referred to the intrinsic axes, these two quantities are shown to reach their extreme values. The results are illustrated by means of an example.

Burrow-centered neural model for burrow surveillance in fiddler crabs

A fiddler crab can estimate how close an intruder is from its burrow [1]. It is believed that crabs use visual information as well as path integration to process that estimation. The fiddler crab Uca vomeris defend their burrows against intruders and it seems they use a burrow-centered reference coordinate. The crabs respond when an intruder approaches the burrow within some distance of the burrow. There are several possible cues to estimate the distance between the intruder and the burrow entrance by visual information such as disparity, optical flow, image size and the retinal elevation. However, experiments show only specific visual information is related to the burrow surveillance [1]. The retinal position, azimuth and elevation angle of the intruder in view is related to the distance between the intruder and the observer, following the geometric function. The former parameters can determine the intruder-crab distance depending on the crab-burrow distance. Fiddler crabs on leaving home accumulate the distance and direction of the exploring path can determine the homing distance and direction from the current position to the burrow [2]. To determine the distance between an intruder crab and the burrow entrance, we need to use the crab-burrow distance by the path integration as well as the azimuth and elevation angle of an intruder. There has been a suggestion that the burrow surveillance in fiddler crabs may be connected with directionally sensitive neurons and distance neurons [1]. Our experiments with a neural model for a mapping function to determine the intruder-burrow distance shows large errors are observed when the intruder is at the opposite side of the crab, since the far vicinity has a low resolution. Thus, we suggest that the fiddler crab might estimate the boundary distance of the response to defend its burrow rather than accurately calculate the distance of the intruder from the burrow. In addition, the crab can determine how directly an intruder is moving toward its burrow. We can thus build a burrow-centered frame of reference with a circular array of directionally sensitive neurons. The firings of the neurons can be mapped from the retinal position of the intruder, that is, the azimuth and elevation angle of the intruder. From that, the fiddler crab can easily determine whether or not the intruder approaches the burrow. As a result, we can build a model of the crab’s response when an intruder approaches the burrow within some distance of the burrow.

A Simple Calibration Method for the Relationship of the Eye-in-Hand of Robot Vision

The space relationships among flange coordinate, camera coordinate and calibration reference coordinate are analyzed. A simple calibration method for the relationship of the eye-in-hand of robot vision is proposed and corresponding experiment system is designed. The result of experiments shows that this method can work simple and shortcut with higher precision.

A full-Eulerian solid level set method for simulation of fluid–structure interactions

We present a full Eulerian method, termed solid level set (SLS) method, for modeling of a class of fluid–structure interactions (FSI) problems soft solid body can deform significantly but remains nearly incompressible. The SLS method is based on the unified momentum equation framework in which the solid–fluid interactions are modeled by introducing a solid body force term and a solid–fluid interfacial force term into the Navier–Stokes equation. The key idea of the SLS method is that the deformation of the solid body is no longer tracked using a Lagrangian mesh. Instead, the solid body is tracked by introducing a reference coordinate for describing the reference state of the solid body and by introducing three dynamic level set functions on the Cartesian coordinate and one static level set functions on the reference coordinate. The SLS method is easy to implement and addresses several challenges in the simulation of FSIs in which a fixed Cartesian mesh is used for fluid flow and a Lagrangian mesh is used for tracking the solid deformation. The effectiveness of the SLS method is demonstrated by studying two FSI problems. The method is suitable for studying a wide range of problems in microfluidics, e.g., manipulation of cells in confined space and ink-jet printing of biological samples.

Study on the propagation law of shock wave resulting from coal and gas outburst

According to the formation of shock wave resulting from coal and gas outburst, the gas flow of coal and gas outburst was transformed from an unsteady flow to a steady one based on selected appropriate reference coordinates, and the mathematical expressions were then established by applying mass conservation, momentum conservation equation, and energy conservation equation. On this basis, analyzed gas flow mitigation of variable cross-section area and the outburst intensity, and the relations between cross-section area, velocity, and density; the relations between overpressures and outburst intensity were deduced. Furthermore, shock waves resulting from coal and gas outburst and outburst intensity were measured by experimental setup, the overpressure and outburst intensity of different gas pressures were obtained, and the similar conditions of the experiment were numerically simulated. The averaged overpressure and gas flow velocity of variable cross-section under different gas pressures were numerically derived. The results show that the averaged overpressure and outburst intensity obtained from simulation are in good agreement with the experimental results. Moreover, the gas flow velocity of variable cross-sections approximates to the theoretical analysis.